$\backslash [\backslash$text $\{$ Minimize $\}$ Z$=$x$\_\{1\}+$x$\_\{2\}+$x$\_\{3\}+$x$\_\{4\}+$x$\_\{5\}+$x$\_\{6\}+$x$\_\{7\}\backslash ]$ subject to: $\backslash [\backslash$begin$\{$array$\}\{$l$\}\backslash$mathrm$\{$x$\}\_\{2\}-\backslash$mathrm$\{$x$\}\_\{1\}\backslash$geq $12\backslash \backslash \backslash$mathrm$\{$x$\}\_\{3\}-\backslash$mathrm$\{$x$\}\_\{2\}\backslash$geq $8\backslash \backslash \backslash$mathrm$\{$x$\}\_\{4\}-\backslash$mathrm$\{$x$\}\_\{2\}\backslash$geq $4\backslash \backslash \backslash$mathrm$\{$x$\}\_\{4\}-\backslash$mathrm$\{$x$\}\_\{3\}\backslash$geq $0\backslash \backslash \backslash$mathrm$\{$x$\}\_\{5\}-\backslash$mathrm$\{$x$\}\_\{4\}\backslash$geq $4\backslash \backslash \backslash$mathrm$\{$x$\}\_\{6\}-\backslash$mathrm$\{$x$\}\_\{4\}\backslash$geq $12\backslash \backslash \backslash$mathrm$\{$x$\}\_\{6\}-\backslash$mathrm$\{$x$\}\_\{5\}\backslash$geq $4\backslash \backslash \backslash$mathrm$\{$x$\}\_\{7\}-\backslash$mathrm$\{$x$\}\_\{6\}\backslash$geq $4\backslash \backslash \backslash$mathrm$\{$x$\}\_\{\backslash$mathrm$\{$i$\}\},\backslash$mathrm$\{$x$\}\_\{\backslash$mathrm$\{$i$\}\}\backslash$geq $0\backslash$end$\{$array$\}\backslash ]$

Please use Excel Solver to solve the following CPM$/$PERT Model Formation Example from the S$14$ lecture slides. Please submit an Excel file showing your work. Excel cells w$/$o formulas will result in a $"0"$ on the assignment. You can skip the sensitivity analysis